<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
</span>
<span>
.
</span>
{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
<span /><span>
</span><span>
</span>
.
Two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line are;
- 1. Arcs are drawn to cross the given line twice on either side relative to the point
- 2. The perpendicular line is drawn using a straight edge by connecting the small arcs formed using the arcs from step 1, to the point on the line or off the line
Description:
1. One of the first steps is to place the compass on the point and from
point, draw arcs to intersect or cross the given line at two points.
2. The compass is placed at each of the intersection point in step 1 and
(opened a little wider when constructing from a point on the line) arcs are
drawn on one (the other side of the point off the line) side of the line with
the same opening (radius) of the compass to intersect each other.
3. From the point of intersection of the arcs in step 2, a line is drawn with a
straight edge passing through the given point.
Learn more about perpendicular lines here:
brainly.com/question/11505244
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Circumference of a circle - derivation
This page describes how to derive the formula for the circumference of a circle.
Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as
π
=
c
d
Rearranging this to solve for c we get
c
=
π
d
The diameter of a circle is twice its radius, so substituting 2r for d
c
=
2
π
r
If you know the area
Recall that the area of a circle is given by
area
=
π
r
2
Solving this for r
r
2
=
a
π
So
r
=
√
a
π
The circumference c of a circle is
c
=
2
π
r
